In [5]:
import numpy as np
import matplotlib.pyplot as plt

from sklearn.model_selection import train_test_split

from sklearn.linear_model import LinearRegression,SGDRegressor

from sklearn.preprocessing import PolynomialFeatures,StandardScaler

from sklearn.metrics import r2_score

from sklearn.pipeline import Pipeline
In [7]:
X = 6*np.random.rand(200, 1) - 3 
y = 0.8*X**2 + 0.9*X+2+np.random.randn(200,1)

# y = 0.8x^2 + 0.9x + 2 

plt.plot(X,y,'b.')
plt.xlabel("X")
plt.ylabel("y")
plt.show()
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In [12]:
# Train test split
X_train,X_test,y_train,y_test = train_test_split(X,y,test_size=0.2,random_state=2)
In [13]:
# applying linear regression
lr = LinearRegression()
In [15]:
lr.fit(X_train,y_train)
Out[15]:
LinearRegression()
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LinearRegression()
In [16]:
y_pred = lr.predict(X_test)
r2_score(y_test,y_pred)
Out[16]:
0.036128825868604886
In [17]:
plt.plot(X_train,lr.predict(X_train),color='r')
plt.plot(X, y, "b.")
plt.xlabel("X")
plt.ylabel("y")
plt.show()
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In [18]:
# Applying Polynomial Linear Regression
# degree 2
poly = PolynomialFeatures(degree=2,include_bias=True)

X_train_trans = poly.fit_transform(X_train)
X_test_trans = poly.transform(X_test)
In [19]:
print(X_train[0])
print(X_train_trans[0])

[-1.01036874]
[ 1.         -1.01036874  1.02084498]
In [20]:
# include_bias parameter
lr = LinearRegression()
lr.fit(X_train_trans,y_train)
Out[20]:
LinearRegression()
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LinearRegression()
In [21]:
y_pred = lr.predict(X_test_trans)
In [22]:
r2_score(y_test,y_pred)
Out[22]:
0.8588711624388841
In [23]:
print(lr.coef_)
print(lr.intercept_)

[[0.         0.89724437 0.78137739]]
[2.11683801]
In [24]:
X_new=np.linspace(-3, 3, 200).reshape(200, 1)
X_new_poly = poly.transform(X_new)
y_new = lr.predict(X_new_poly)
In [25]:
plt.plot(X_new, y_new, "r-", linewidth=2, label="Predictions")
plt.plot(X_train, y_train, "b.",label='Training points')
plt.plot(X_test, y_test, "g.",label='Testing points')
plt.xlabel("X")
plt.ylabel("y")
plt.legend()
plt.show()
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In [26]:
def polynomial_regression(degree):
    X_new=np.linspace(-3, 3, 100).reshape(100, 1)
    X_new_poly = poly.transform(X_new)

    polybig_features = PolynomialFeatures(degree=degree, include_bias=False)
    std_scaler = StandardScaler()
    lin_reg = LinearRegression()
    polynomial_regression = Pipeline([
            ("poly_features", polybig_features),
            ("std_scaler", std_scaler),
            ("lin_reg", lin_reg),
        ])
    polynomial_regression.fit(X, y)
    y_newbig = polynomial_regression.predict(X_new)
    plt.plot(X_new, y_newbig,'r', label="Degree " + str(degree), linewidth=2)

    plt.plot(X_train, y_train, "b.", linewidth=3)
    plt.plot(X_test, y_test, "g.", linewidth=3)
    plt.legend(loc="upper left")
    plt.xlabel("X")
    plt.ylabel("y")
    plt.axis([-3, 3, 0, 10])
    plt.show()
In [27]:
polynomial_regression(350)

D:\New folder\jupyter\Lib\site-packages\sklearn\utils\extmath.py:1066: RuntimeWarning: overflow encountered in square
  temp **= 2
D:\New folder\jupyter\Lib\site-packages\numpy\core\fromnumeric.py:88: RuntimeWarning: overflow encountered in reduce
  return ufunc.reduce(obj, axis, dtype, out, **passkwargs)
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In [28]:
poly.powers_
Out[28]:
array([[0],
       [1],
       [2]], dtype=int64)
In [29]:
# Applying Gradient Descent

poly = PolynomialFeatures(degree=2)

X_train_trans = poly.fit_transform(X_train)
X_test_trans = poly.transform(X_test)

sgd = SGDRegressor(max_iter=100)
sgd.fit(X_train_trans,y_train)

X_new=np.linspace(-2.9, 2.8, 200).reshape(200, 1)
X_new_poly = poly.transform(X_new)
y_new = sgd.predict(X_new_poly)

y_pred = sgd.predict(X_test_trans)

plt.plot(X_new, y_new, "r-", linewidth=2, label="Predictions " + str(round(r2_score(y_test,y_pred),2)))
plt.plot(X_train, y_train, "b.",label='Training points')
plt.plot(X_test, y_test, "g.",label='Testing points')
plt.xlabel("X")
plt.ylabel("y")
plt.legend()
plt.show()

D:\New folder\jupyter\Lib\site-packages\sklearn\utils\validation.py:1143: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().
  y = column_or_1d(y, warn=True)
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In [30]:
# 3D polynomial regression
x = 7 * np.random.rand(100, 1) - 2.8
y = 7 * np.random.rand(100, 1) - 2.8

z = x**2 + y**2 + 0.2*x + 0.2*y + 0.1*x*y +2 + np.random.randn(100, 1)
# z = x^2 + y^2 + 0.2x + 0.2y + 0.1xy + 2
In [31]:
import plotly.express as px
df = px.data.iris()
fig = px.scatter_3d(df, x=x.ravel(), y=y.ravel(), z=z.ravel())
fig.show()
In [33]:
lr = LinearRegression()
lr.fit(np.array([x,y]).reshape(100,2),z)

x_input = np.linspace(x.min(), x.max(), 10)
y_input = np.linspace(y.min(), y.max(), 10)
xGrid, yGrid = np.meshgrid(x_input,y_input)

final = np.vstack((xGrid.ravel().reshape(1,100),yGrid.ravel().reshape(1,100))).T

z_final = lr.predict(final).reshape(10,10)
In [34]:
import plotly.graph_objects as go

fig = px.scatter_3d(df, x=x.ravel(), y=y.ravel(), z=z.ravel())

fig.add_trace(go.Surface(x = x_input, y = y_input, z =z_final ))

fig.show()
In [41]:
X_multi = np.array([x,y]).reshape(100,2)
X_multi.shape
Out[41]:
(100, 2)
In [60]:
poly = PolynomialFeatures(degree=30)
X_multi_trans = poly.fit_transform(X_multi)
In [56]:
lr = LinearRegression()
lr.fit(X_multi_trans,z)
Out[56]:
LinearRegression()
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LinearRegression()
In [57]:
X_test_multi = poly.transform(final)
In [58]:
z_final = lr.predict(X_multi_trans).reshape(10,10)
In [59]:
fig = px.scatter_3d(x=x.ravel(), y=y.ravel(), z=z.ravel())

fig.add_trace(go.Surface(x = x_input, y = y_input, z =z_final))

fig.update_layout(scene = dict(zaxis = dict(range=[0,35])))

fig.show()
In [ ]: